Getting There And Back

In this puzzle, we challenge you to determine the difference in air speeds when flying into and out of the wind.

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You are traveling by air between two cities that are 1,600 km (1,000 mi) apart. Your plane flies at a speed of 800 km/h (500 mph). If there is no wind, your flying time is two hours each way. The round trip takes four hours.

But what if there is wind? Let's say that on the way from City A to City B there is a headwind of 200 km/h (120 mph). This means that your ground speed is only 600 km/h (370 mph). But on the way back you have a tailwind of 200 km/h, so your ground speed is 1,000 km/h (620 mph).

How does the wind affect your round-trip time? Is it longer than, shorter than, or the same as in calm conditions?

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Course:

Math [1]

Result/Solution(s)

Solution: Getting There and Back Math Puzzle

Many people immediately answer that the flying time is the same. What you lose because of a headwind in one direction should be the same as what you gain owing to a tailwind on the return trip. But if you do the calculations, you'll see that this isn't the case.

With no wind, the round trip will take 4 hours: 1,600 km (1,000 mi) at 800 km/h (500 mph) means the trip is 2 hours each way.

With a 200 km/h headwind, the ground speed is 600 km/h. The time it takes to cover 1,600 km is
: 1,600 km / 600 km/h ( 370 mph) = 2.67 hours, or 2 hours and 40 minutes
In the other direction the ground speed is 1,000 km/h (620 mph) so the time it takes to go 1,600 km is
: 1,600 km / 1,000 km/h = 1.6 hours, or 1 hour and 36 minutes
The total travel time is 4 hours and 16 minutes. Let's say that the wind speed is increased to 400 km/h (250 mph). Then the ground speed with a tailwind is 1,200 km/h (750 mph), and the travel time in that direction is
: 1,600 km / 1,200 km/h = 1.33 hours, or 1 hour and 20 minutes
In the other direction the ground speed is 400 km/h so the travel time is
: 1,600 km / 400 km/h = 4 hours.
The total travel time is 5 hours and 20 minutes. This is an hour longer than with the wind at 200 km/h.

Try the calculation with different wind speeds and see what your results are. What would happen to the total time for the trip if the wind speed were 800 km/h?